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Richard has $\$652$ in his account and is planning a road trip. He looks at how expensive hotels and sightseeing costs are in certain cities, planning accordingly:




City		Cost ${ }^{(\$)}$

Detroit		196.87

Pittsburgh		180.32

St. Paul		102.87

Cincinnati		155.81

Richmond		211.86






When Richard makes the calculations, he finds he does not have enough money to visit each city. What is the cheapest city that Richard can drop to avoid overdrawing his account?


ARichmond
BDetroit
CPittsburgh
DCincinnati

Verified Answer :

  • Calculate the total cost of all five cities: \(\$847.73\).
  • Determine the deficit compared to the budget: \(\$847.73 - \$652 = \$195.73\).
  • Identify cities with a cost at least \(\$195.73\), which are Detroit (\(\$196.87\)) and Richmond (\(\$211.86\)).
  • Select the cheapest of these cities, which is Detroit, to ensure the remaining total is within budget. The final answer is \(\boxed{b}\).

Explanation

  1. Calculate Total Cost

To find out which city Richard should drop to avoid overdrawing his account, we first need to determine the total cost of visiting all five cities. We are given the following costs:

  • Detroit: \(\$196.87\)
  • Pittsburgh: \(\$180.32\)
  • St. Paul: \(\$102.87\)
  • Cincinnati: \(\$155.81\)
  • Richmond: \(\$211.86\)

The total cost is the sum of these individual costs:
\[T = 196.87 + 180.32 + 102.87 + 155.81 + 211.86 = \$847.73\]

  1. Calculate the Deficit

Richard has a budget of \(\$652.00\). The current total cost exceeds his budget, so we must calculate the deficit that needs to be covered by dropping a city:
\[\text{Deficit} = \text{Total Cost} - \text{Budget} = 847.73 - 652.00 = \$195.73\]
Richard must drop at least one city such that the cost of that city is at least \(\$195.73\) to ensure his remaining expenses are within his \(\$652.00\) budget.

  1. Identify the Cheapest City to Drop

Now, we identify all cities whose costs meet or exceed the deficit of \(\$195.73\):

  • Detroit: \(\$196.87\)
  • Richmond: \(\$211.86\)

Both cities have a cost greater than \(\$195.73\). Since the objective is to drop the cheapest city that satisfies this condition, we compare the costs of these two cities:

  • Detroit cost: \(\$196.87\)
  • Richmond cost: \(\$211.86\)

Comparing these, Detroit is the cheaper option. Therefore, by dropping Detroit, Richard's new total cost would be \(847.73 - 196.87 = \$650.86\), which is within his budget of \(\$652.00\). Thus, the cheapest city Richard can drop is Detroit.

  1. Final Conclusion

After evaluating the costs, the total expenditure exceeds the budget by \(\$195.73\). Comparing the potential savings from dropping each city, the city of Detroit is the most cost-effective one to remove while keeping the remaining travel expenses within the budget. Therefore, the correct option is b.

The final answer is \(\boxed{b}\).

Examples

Budget management is a critical skill in everyday financial planning. For instance, if you are planning a group project or a trip and find that the total estimated expenses exceed your available funds, you must identify which non-essential or most expensive components can be omitted to align with your financial limit. By calculating the total deficit and identifying the most cost-effective items to remove, you can successfully balance your budget without overdrawing your account. This is the same principle applied to balancing a travel itinerary with fixed costs in each city.

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